A thermionic cathode is a cathode that exhibits thermionic emissions.
Thermionic emission is the emission of charged particles (typically electrons) from a conductor at high temperature. At sufficiently high temperature, some significant fraction of electrons exceed the energy required (the work function) to escape the atom from the Fermi level. Thermionic emission is governed by the Richardson-Dushman equation. Examples of thermionic emissions include filaments (e.g. as in mass spectrometry). See also Wikipedia: Thermionic emission.
The CPO software provides space-charge methods for simulating cathode emissions effects, including thermionic emissions. See Cathodes in CPO.